All the goalmouth incidents during the opening 45 minutes involved Kieron Renton in the visitors' goal. He foiled Derek Ure by pushing out the Shire midfielder's forceful shot, and although Steven Dymock got his head to the loose ball, Paul Kaczan was on hand to clear off the goal-line.
Renton pulled off one or two excellent saves, and one in particular stood out when he raced off his line to block Carl Thywissen on the edge of the penalty box.
Whatever new manager Brian Irvine said to his players at half-time seemed to work as the visitors were a more determined outfit after the restart.
The opening goal was set up by Adam Nelson, who provided an opening for Stuart Cumming to fire a low shot past Derek Jackson inside his left-hand upright.
Nelson himself increased the visitors' lead with a bit of luck as his shot took a wicked deflection off the unfortunate Mark Tyrrell to leave Jackson stranded.
Cummings came close again for Elgin with a header against the crossbar, but there were to be no more chances and Elgin settled for a comfortable 2-0 score-line at the close.